SPECKLE INTERFEROMETRY USING A HARDWIRED AUTOCORRELATOR By Jeremy Charles Hebden, B.Sc. May 1984 A thesis submitted for the degree of Doctor of Philosophy of the University of London and for the Diploma of Membership of the Imperial College of Science and Technology. Astronomy Group, Blackett Laboratory, Imperial College, London SW7 2BZ. I wish to dedicate this thesis to my parents, who deserve it, and to Tottenham Hotspur Football Club, who too often don’t. Acknowled gements I wish to extend my thanks to my supervisor, Dr Brian L. Morgan, and to Mr Harry Vine for their generous help and guidance. Sincere thanks also to numerous other members of the group both past and present who have helped to make life so interesting and enjoyable during the course of this research. I am very grateful to the Science and Engineering Research Council for the provision of an SERC Research Studentship. Finally I would like to thank Dr Tony Canas for his advice and assistance in the formatting and printing of this thesis. This thesis was produced using the Format-80 word processor. 3 * Abstract Stellar speckle interferometry is a technique which enables diffraction limited information to be obtained from large telescopes despite the presence of atmospheric turbulence which normally limits resolution to about one arcsecond or worse. The information is retained in quasi-instantaneous images whose exposure times are short in comparison with the lifetime of the atmospheric perturbations on the wavefront of light from a star. Such images have a speckled appearance. This thesis describes research concerning real-time digital analysis of speckle images using a hardwired autocorrelator. A device called a speckle interferometer was built which is designed to produce high magnification bandwidth limited images of low light level stellar objects using large telescopes. The images are focussed from the output phosphor of a four stage image intensifier onto the tube of a television camera. They are then recorded onto video tape and may be processed in real-time at a rate of twenty five frames per second. The hardwired autpcorrelator produces a two-dimensional spatial autocorrelation which is stored in an 8K by 20 bit integrating memory. A microcomputer based data reduction system has been developed which enables data to be displayed in numerous forms and stored on magnetic disc. In addition several calculations such as azimuthal averaging may be performed. A system of data analysis has also been developed which involves the calculation of computer generated models. System development has been complemented by a very active programme of observations. Recent published work includes the results obtained from observations of the Seyfert nucleus of N G C 1068, the extremely compact object R136a, the bright and variable star Eta Carinae and the binary star in the centre of the Red Rectangle nebula. Additionally results of binary star observations as part of the Hipparcos project have been published and a number of asteroid observations have been made. 4 » Speckle Interferom Interferom etry etry Using Using A AHardwired Hardwired A A utocorrelatorSpeckle utocorrelator Contents Page Title page 1 Dedication 2 Acknowledgements 3 • Abstract 4 List of contents 5 List of figures 8 Chapter One : Introduction Section Page 1-1 High resolution optical astronomy 11 1-2 Hardwired data processing 14 1- 3 Related techniques 14 Chapter Two : Theoretical Review Section Page 2- 1 Introduction 18 2-2 Theoretical outline 20 2-3 Signal to noise ratio 22 2-4 Autocorrelation 24 2-5 Autocorrelation of speckle images 25 2-6 Crosscorrelation 29 2- 7 Phase retrieval 30 Chapter Three : The Imaging System And Digital Analysis Hardware Section Page 3- 1 The speckle interferometer 35 5 # Section Page 3-2 The atmospheric dispersion compensation prisms 37 3-3 The sensor system 41 3-4 The shutter 43 3-5 Magnification and image scale 45 3-6 Design requirements of a hardwired real-time autocorrelator 46 3-7 Operation of the hardwired real-time autocorrelator 48 3-8 System developments 50 3-9 The hardwired cross correlator 53 3-10 Image monitoring and data display 55 3-11 Operational procedure 57 Chapter Four : Data Reduction Procedure Section Page 4-1 The profile selector 61 4-2 Mainframe computer systems 62 4-3 Requirements of a permanent data reduction system 63 4-4 The Apple ] [ and peripheral devices 64 4-5 Data reduction software 65 4-6 Operational procedure 70 4-7 Limiting magnitude 72 4-8 System calibration 73 4-9 Reference star observations 75 Chapter Five : Data Analysis Section Page 5-1 Introduction 77 5-2 Binary star analysis 78 5-3 Seeing component modelling 81 5-4 The photon spike 84 5-5 Speckle component modelling 85 6 % Section Page 5-6 Angular diameter measurement of centro-symmetric objects 91 5-7 Investigation of non-symmetricobjects 93 5-8 Calibration observations 93 5- 9 Sources of error 97 Chapter Six : Astronomical Results Section Page 6- 1 Introduction 100 6-2 Hipparcos stars 100 6-3 Asteroids 104 6-4 The Seyfert nucleus of N G C 1068 108 6-5 R136a 111 6-6 Eta Carinae 115 6-7 The binary star in the Red Rectangle 119 6-8 Preliminary results concerning NG C 2346 123 6- 9 Other observations 125 Chapter Seven ; Conclusions And Future Work Section Page 7- 1 Technique 129 7-2 Apparatus 131 7-3 Results 133 Page Publications 137 References 166 7 ' 4 List of Figures Figure Description 2.1 A short exposure image of an unresolved star 2.2 Autocorrelation by area overlap 2.3 Autocorrelation by vector distribution 2.4 A n autocorrelation profile 2.5 a) An idealised speckle image of a binary star ♦ b) A secondary peak situated within an autocorrelation profile 3.1 : The speckle interferometer 3.2 : Refraction by the atmosphere 3.3 Light path through a double prism 3.4 : Gain curves of the A and B image intensifiers 3.5 Output and gain of the T V camera plumbicon tube 3.6 : The shutter 3.7 : Autocorrelation vector window 3.8 : Operation of the hardwired real-time autocorrelator 3.9 : A T V line containing faint and bright events (schematic) 3.10 : The hardwired autocorrelator 3.11 : The Anglo-Australian Telescope, Siding Spring 4.1 : a) Selected profiles b) The LED display 4.2 : Autocorrelation array and profile angle 4.3 : Three displays of the autocorrelation of the binary star ADS 1123 5.1 Isolating a secondary peak 5.2 Seeing component modelling 5.3 A photon spike 5.4 Convolution between arrays 5.5 Model image profiles 5.6 Autocorrelated model speckles 5.7 Data analysis performed on the autocorrelation of an unresolved star 8 Figure Description 5.8 The data reduction technique applied to the autocorrelation of Europa 5.9 The 1.9m Kottamia telescope in Egypt 6.1 Secondary peaks in three Hipparcos star autocorrelation profiles 6.2 The 1.8m Perkins telescope, Lowell Observatory, Arizona 6.3 Azimuthally averaged autocorrelation profiles of a point source and Herculina 6.4 Isolated speckle components of a point source and Herculina 6.5 An azimuthally averaged autocorrelation profile of the nucleus of N G C 1068 6.6 The 30 Doradus nebula 6.7 An azimuthally averaged autocorrelation profile of R136a 6.8 The nebula N G C 3372 6.9 An azimuthally averaged autocorrelation profile of Eta Carinae 6.10 Position angle and separation measurements of the binary star in the Red Rectangle nebula 6.11 The secondary peak contained in the autocorrelation of H D 44179 6.12 An azimuthally averaged autocorrelation profile of the central star in the nebula N G C 2346 6.13 a) The estimated speckle component of the central star in the nebula N G C 2346 b) The estimated object intensity distribution Chapter One % Chapter One : Introduction 1-1 High resolution optical astronomy The angular resolution of large telescopes at visible wavelengths is drastically reduced by the effects of atmospheric turbulence. The image of a star, usually called the seeing disc, has an angular diameter which varies approximately from 0.5 arcseconds, during periods of good seeing, to 10 arcseconds or more, depending on the atmospheric conditions. A seeing disc diameter of one arcsecond is equivalent to the resolution limit at visible wavelengths of a telescope with an aperture of 12cm in diameter. Hence even at the time of Newton and Herschel telescopes were being built whose resolution was limited by the atmosphere rather than by telescope optics. The desire to overcome the atmospheric degradation of stellar images has resulted in the introduction of the Space Telescope, a 2.4m aperture instrument which is due to be placed in orbit around the Earth in 1986. However, a few enterprising physicists have succeeded in developing techniques which can, to some degree, avoid the damaging effects of atmospheric turbulence on ground based observations. The idea of using optical interferometry to determine the structure of stellar objects was first suggested by Fizeau [66] in 1868. Several years later this suggestion was brilliantly applied by Michelson [67] , resulting in the development of a single telescope synthetic aperture system. In 1921 this was developed still further by Michelson and Pease [80] into the long baseline interferometer (see section 1-3). A twenty foot baseline interferometer, mounted on the 100-inch telescope at Mount Wilson, enabled Michelson and Pease to determine the angular diameter of Betelgeuse. During the following ten years Pease [73] reported measurements of several other bright red giants and supergiants whose angular diameters lay in the range from 0.02 to 0.05 arcseconds. However, as mentioned by Hanbury Brown [84] , a critical assessment of the accuracy of the results was never published.